Matrix-valued harmonic functions on groups. (English) Zbl 1011.31004
The authors study the basic structures of matrix-valued harmonic functions on locally compact groups. They show that the bounded matrix-valued harmonic functions on a group form a Jordan triple system and they determine its structure. They also show that Liouville property implies amenability of the group. They characterize the unbounded matrix-valued harmonic functions on abelian groups.
Reviewer: M.Banulescu (Bucureşti)
MSC:
| 31C05 | Harmonic, subharmonic, superharmonic functions on other spaces |
| 43A70 | Analysis on specific locally compact and other abelian groups |
| 22D05 | General properties and structure of locally compact groups |
| 17A40 | Ternary compositions |
Keywords:
matrix-valued harmonic functions on locally compact groups; Jordan triple system; unbounded matrix-valued harmonic functions on abelian groupsReferences:
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